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Perimeter of Polygons: Regular & Irregular

Polygon perimeter is side addition at heart. Regular polygons add the shortcut P = n × s, with notes for land sketches and composite outlines.

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Geometry shapes and measuring tools for perimeter guides

Quick Answer

Polygon perimeter is the sum of all side lengths around the closed figure.

Formula

  • Regular polygon: P = n × s
  • Irregular: add each measured side

Introduction

The home Perimeter Calculator includes pentagon, hexagon, octagon, irregular quadrilateral, and custom regular polygon modes for class and quick field checks.

Start by tracing the outline. Count how many sides you cross. That habit prevents leaving out one edge on an irregular lot drawing.

Advanced coordinate geometry and proofs can wait until perimeter totals are comfortable. This page stays with measuring and adding.

Symbol reference for rectangles and circles appears in our perimeter formula guide when you mix polygons with simpler shapes on one worksheet.

Worked totals for pentagons, hexagons, and quadrilaterals also appear in perimeter examples if you want parallel numbers to check your manual sum.

Main Content

Regular and irregular polygons

A polygon is a closed plane figure with straight sides. Perimeter always means adding those sides, whether or not the shape looks regular.

Regular polygons have equal sides and equal angles. The shortcut P = n × s counts every matching edge in one multiplication.

Irregular polygons need a raw sum. A four-sided lot with sides 40, 55, 38, and 47 ft has perimeter 180 ft with no shortcut beyond addition.

Composite figures on plans may hide a rectangle inside an L-shape. Trace only the outer boundary the fence will follow.

Regular vs irregular

  • Regular: P = n × s
  • Irregular: P = s₁ + s₂ + … + sₙ

Do not add internal edges shared by two rooms inside a building outline. Perimeter follows the outer loop only.

Land surveying often chains several straight segments; that is polygon perimeter in the field, even when the plot is not a textbook regular hexagon.

Stop signs and hexagonal tiles are everyday regular hexagons. A stop sign with side 12 in has perimeter 72 in when you model it as six equal edges.

Step-by-step for polygons

  1. Count sides Mark each vertex on your sketch so you know how many edges the boundary has.
  2. Measure or read lengths Use one unit. Convert before adding when the deed mixes feet and inches.
  3. Add or multiply Multiply only when every side is equal and you know n. Otherwise add explicitly.
  4. Verify Use the matching mode on the home calculator when n or side labels match a preset shape.

Examples

Regular octagon, side 3 m: P = 8 × 3 = 24 m.

Irregular quadrilateral sides 6, 7, 8, 9 ft: P = 30 ft.

Regular polygon mode with n = 9 and side 4 models a nonagon with P = 36 in class.

Pentagon with side 10 cm: P = 50 cm when all five edges match.

FAQ

Do interior angles affect perimeter?
Not directly. Perimeter depends on side lengths along the boundary, not on angle measures alone.
Is a rectangle a polygon?
Yes. It is a quadrilateral, which is a four-sided polygon. You may use P = 2(l + w) instead of adding four terms.
When should I not use P = n × s?
When sides differ or you do not know how many equal edges the real object has. Irregular outlines need a straight sum.

Conclusion

Name the polygon, count sides, then add or multiply as the shape allows.

Open polygon modes on the home page for quick checks on regular figures.

Calculate polygon perimeter